Spatial Predator–Prey Waves

Turing instability in predator-prey systems: when predators diffuse much faster than prey, the spatially homogeneous coexistence equilibrium can become unstable to spatial perturbations, generating stationary or traveling waves. The condition requires D_pred ≫ D_prey. Here, prey (green) follows ∂u/∂t = D_u∇²u + αu − βuv; predator (red) ∂v/∂t = D_v∇²v + βuv − δv.